President Obama is mulling what could well be the most important decision of his second term – nominating Ben Bernanke’s replacement as Federal Reserve chairman.

Bernanke, whose second four-year term is set to end in January, has presided over perhaps the most dramatic period in the century-long history of the Fed, the mostly autonomous central bank that sets interest rates and controls the supply of money for the U.S. economy.

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The credit crisis that emerged in late 2007 with a downturn in the housing market eventually led to a near-collapse of the financial system and the deepest economic recession since the Great Depression.

In response, Bernanke drove the short-term interest rates under its control to near zero, and unleashed three rounds of bond buying that have injected massive amounts of fresh money into the economy to keep inexpensive loans flowing in the economy.

The economic recovery, while slower than hoped, has continued since late 2009, and Bernanke has vowed to keep rates unusually low at least until the unemployment rate, now at 7.4%, falls to 6.5%.

The stakes surrounding Obama’s choice for Bernanke’s successor are unusually high. For one thing, the Fed chairmanship doesn’t frequently become vacant. Since 1979, there have been only three leaders of the Fed.

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Paul Volcker was put forward by President Jimmy Carter and is credited with slaying runaway inflation and setting the scene for the ‘80s economic renaissance through punitively high interest rates. Alan Greenspan used opportunistic rate cuts to help the eoconmy through the 1987 stock-market crash and 1990 recession, ushering in the ‘90s boom.

Bernanke has also presided over an unusually aggressive stimulus policy, which continues for the moment in the form of $85 billion of Fed purchases of Treasury and mortgage bonds per month. His programs have ballooned the Fed’s assets to nearly $4 trillion from less than $1 trillion before the financial crisis.

At some point, Fed stimulus must be wound down in response to further economic improvement, or perhaps a pickup in inflation. At the moment, financial markets are nervously watching for clues of the Fed’s intentions for dialing back its “quantitative easing” campaign of monthly bond purchases – with many economists expecting this to occur in September.

The new Fed chair will have to manage this process, while also assuring world investors, consumers and businesspeople that he or she stands ready to respond assertively to changing economic fortunes. With interest rates around the developed world already close to zero, central bankers’ spoken messages about future policy carry enormous weight.